用拉普拉斯变换重新解读差分隐私，揭示其内在数学结构。
Laplace Transform Interpretation of Differential Privacy
- 将差分隐私表示为隐私损失分布的拉普拉斯变换，建立新分析视角。
- 证明了ε-δ差分隐私在所有ε值下自适应组合定理严格紧致。
- 解决子采样下f-DP对称性问题，统一各类差分隐私定义。
我们引入差分隐私（DP）概念的拉普拉斯变换表达形式，该形式在多个相关工作中以积分或期望形式出现。认识到这一表达为拉普拉斯变换，可借助时频域对偶性来全新理解DP性质。利用此视角，我们揭示了( q, ρ(q) )-Rényi DP曲线与( ε, δ(ε) )-DP曲线互为拉普拉斯与逆拉普拉斯变换关系，表明Rényi散度在复数阶 q = γ + iω 下仍有定义。基于该分析，我们证明了一个适用于所有ε值的精确紧致自适应组合定理。此外，解决了子采样下f-DP对称性问题，从而实现了所有函数型差分隐私概念之间的等价性。
原文摘要 · Abstract (English)
We introduce a set of useful expressions of Differential Privacy (DP) notions in terms of the Laplace transform of the privacy loss distribution. Its bare form expression appears in several related works on analyzing DP, either as an integral or an expectation. We show that recognizing the expression as a Laplace transform unlocks a new way to reason about DP properties by exploiting the duality between time and frequency domains. Leveraging our interpretation, we connect the $(q, ρ(q))$-Rényi DP curve and the $(ε, δ(ε))$-DP curve as being the Laplace and inverse-Laplace transforms of one another. This connection shows that the Rényi divergence is well-defined for complex orders $q = γ+ i ω$. Using our Laplace transform-based analysis, we also prove an adaptive composition theorem for $(ε, δ)$-DP guarantees that is exactly tight (i.e., matches even in constants) for all values of $ε$. Additionally, we resolve an issue regarding symmetry of $f$-DP on subsampling that prevented equivalence across all functional DP notions.
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